Fast Unimodular Counting

Authors:
John Mount
Affiliations:
@TheMoment, Inc., 2755 Campus Dr., Suite 145, San Mateo, CA 94403, USA (e-mail: ja_mount@pacbell.net)
Venue:
Combinatorics, Probability and Computing
Year:
2000

Citing 3
Cited 2

Theory of linear and integer programming

Theory of linear and integer programming
On vector partition functions

Journal of Combinatorial Theory Series A
Sampling contingency tables

Random Structures & Algorithms

Approximately counting integral flows and cell-bounded contingency tables

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximately Counting Integral Flows and Cell-Bounded Contingency Tables

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper describes methods for counting the number of nonnegative integer solutions of the system Ax = b when A is a nonnegative totally unimodular matrix and b an integral vector of fixed dimension. The complexity (under a unit cost arithmetic model) is strong in the sense that it depends only on the dimensions of A and not on the size of the entries of b. For the special case of ‘contingency tables’ the run-time is 2O(√dlogd) (where d is the dimension of the polytope). The method is complementary to Barvinok's in that our algorithm is effective on problems of high dimension with a fixed number of (non-sign) constraints, whereas Barvinok's algorithms are effective on problems of low dimension and an arbitrary number of constraints.